Antonio Conte is looking to strengthen his squad, and could raid his former club for the Dutch defensive duo.
De Vrij is out of contract at the end of the season, and Spurs may fancy their chances at landing the centre-back in January, whilst Dumfries still has two and a half years left to run on his deal.
Speaking to Football Insider, Robinson claimed that both are necessary in the next two windows to strengthen the Spurs backline.
“Dumfries would make a huge difference,” he stated.
“De Vrij is also a top player but they can probably get away with the centre-halves they have got until the end of the season.
“Right wing-back is one of the top priorities. It’s obvious that Conte is looking in that area.
“If they could get both those players through the door it would be a massive difference. It seems unlikely they would be able to in January though.
“Both players are proven at the very top level. They both know the system so you would expect them to settle in quickly. That is why the manager probably wants them.”
Spurs desperately need reinforcements in both areas, with Eric Dier and Emerson Royal both receiving criticism for their poor performances this season, and signing two experienced players could make a huge difference.
Both players can settle quickly to life under Conte, with De Vrij already having experience under the Italian coach, and would arguably provide upgrades on the current Spurs players in their positions.
Dumfries ranks in the top 6% of fullbacks for aerial duels, shots, and attacking penalty area touches, which resembles a significant improvement over Royal, whilst De Vrij would arrive as a title winner with over 350 senior appearances to his name.
If these two arrive at the club in January, then Spurs would stand a much better chance of a top-four finish.